Implementing model solutions

I just came across this blog post which talks about another layer of doing math modeling. The basis of my blog is that you should try to make sure you solve the right problem, otherwise you can't hope to get a good solution. What the blogger points out is that even if you solve the right problem, that does not guarantee that the solution will be implemented correctly. His example comes from doing retail stock forecasting. He describes several of the ways his customers may use the information gleaned from the software to make inappropriate decisions.

There are similar issues in my research area. I work on "the newsvendor problem" where you sell newspapers during the day. You start by choosing a quantity of newspapers y to buy at the beginning of the day for c dollars each, and sell them for r apiece. If you run out early, you have a lost sales cost of e, and if you have leftovers you can recycle them for v each. Empirical studies find that even when participants are trained about the optimal order quantity, they tend to over-order.

So how to resolve these issues? Effective communication skills are a key starting point. By asking the right questions of practitioners, modelers can ensure both that they solve the right problem and do their best to make sure that the solutions are taken seriously.

A case for paying friends $0.50 per mile

Giving friends money for gas is the default offer in college. The logic goes something like this: "Most of the costs to drive other than gas are either negligible or fixed, so paying for gas is close to fair." Yet, the cost of gas works out to around 15 cents per mile while the government estimate of the cost of driving is 57.5 cents per mile. The quote from the IRS website is that these costs include "the fixed and variable costs of operating an automobile, including depreciation, insurance, repairs, tires, maintenance, gas and oil." The IRS also says that moving or medical miles have a rate of 23 cents per mile to cover strictly the "variable costs such as gas and oil."

Based on the law, that suggests paying friends 23 cents per mile if they are making a special trip for you. However, an issue arises when you actually look at the list of "fixed costs." Clearly repairs due to normal wear and tear, depreciation, tires, and maintenance all are highly dependent on the actual number of miles driven. The only thing on the explicit list that is strictly a fixed cost is insurance. But, what is insurance actually for? Insurance covers (hopefully most) costs in the event of an accident. While registration costs are truly fixed since you either keep your car legally registered or not, insurance costs are an attempt to reduce risk.

It may be possible to separate the truly variable costs from the truly fixed and get a more accurate rate to pay friends. But I would argue that the government rate is a much better approximation of the variable cost of driving than simply paying for gas.

Turkers

In 1770, a wonderful machine was revealed. The Turk (also known as Automaton Chess Player) was a chess-playing machine that beat various famous opponents.

If you've ever heard of "Amazon Mechanical Turks," this machine is where they got their name. Amazon Mechanical Turk is a marketplace where people who are willing to do "Human Intelligence Tasks" choose from available tasks which companies are willing to pay to have done. These tasks are generally things computers are not great at -- classifying a sentence as funny or not for instance -- but that humans can do easily. As you probably guessed by now, the original Turk was not actually a machine, but in fact had a chess master hide inside it. I highly recommend reading the wikipedia link, how elaborate the hoax was made my day.

So how does this relate to decision making? First off, you might use the data directly to make decisions. However, while computers may not be good at determining if a sentence is funny, you can train them on data to predict whether a sentence is funny. And it turns out you can use Turkers to generate that training data! Kartik Hosanagar used Natural Language Processing algorithms in conjunction with Turker-generated data on various corporate Facebook posts to attempt to infer what drives consumer engagement (the abstract is available here). This seems like a really cool technique which can be used to inform a whole lot of decision making in the future.

Liver Allocations

Today my department had Sommer Gentry give a presentation on her work on liver transplants, an area I previously knew very little about. The basic idea is that because livers only last up to 8 hours after the donor dies, we can't simply allocate to whoever in the country needs it the most. Instead, historically there were 59 DSA (districts) and 11 regions (collections of districts). So within each DSA, an available liver is allocated to whoever needs it most.

This seems like a pretty good way to handle things until you know that liver availability does not necessarily match up with demand. Sommer's research has to do with coming up with collections of districts which will lead to a more equitable allocation across the US.

The big takeaway to me of her presentation was that transparency is key if you're actually hoping to have policy change because of your optimization results. She explained that some things which you would naturally want to have as an objective (distance organs travel for instance), end up as constraints when you want a model you can explain to anyone. This was particularly important since, as you can see in the video below, some entities are major losers in a more fair world. If the stakeholders can't find a problem with the process, just the outcome, then it will be a lot easier to achieve change!

I really enjoyed her presentation, and encourage you to watch the entire video (This seems to be a more mathematical version of the presentation I saw). The jump is set to her presenting a comparison of her solution vs. the current one in a way that visually shows the difference in fairness, which hits on transparency once again.

Feel free to post questions about the problem below!

Shipping Logistics

When making decisions I try to think about the resources I'm using, rather than just the cost. For example, last weekend I was shopping online for a few things I need soon, but not immediately. I decided to hold off on making the purchase until after Christmas so as avoid further overloading the system. I had already read a couple articles explaining that UPS has temporarily nearly doubled their trucking fleet, and added a lot of extra workers and planes too. But it still seemed like a good idea to wait.

Based on apologies by UPS and FedEx earlier this week, I made the right choice. Both shipping companies were unable to make all the deliveries they had promised in time for Christmas. You may wonder why I think one more package even matters? It highly depends on where that package appears on the system. It is always possible that my package would have been the difference between needing one truck between Chicago and Detroit, versus two. 

If you think this idea is interesting, I highly recommend reading this link on traffic congestion (though the formatting leaves a bit to be desired). The author provides an interesting perspective on how individuals can dramatically influence a congested road system.

The Anchoring Effect

I've found myself very busy the last couple months. However, while working on a homework assignment I was reminded of this old blog post describing the anchoring effect http://youarenotsosmart.com/2010/07/27/anchoring-effect/.

My interpretation of this concept is that "value" has a lot less to do with what an object is worth to you, and a lot more to do with what your alternatives. If you lived in an alternate reality where toilet paper cost twice as much, how would that change your behavior? What about a world where it cost half as much?

This does not mean that everything is without value, but you have to create your own metric if you want to make rational decisions. As a kid, my brother and I played the card game Magic the Gathering, and there was a store we could get (common) cards from for $0.05 each. We could then translate prices of other things into magic cards. Is it worth getting this toy? Well, is it worth 200 magic cards?

As an adult (who is reasonably privileged) making consistent decisions is a lot harder. There are a lot more things I could conceivably purchase, but which ones are "worth it" is harder to determine. Is a vacation trip to Alaska worth working a month longer before retirement? It's harder to compare.

The article itself has a somewhat different take on the subject, but I highly recommend giving it a read.

Breaking down optimal decision making

In my previous post, I described a possible decision making scenario, and how things might progress. However, there are a lot of motivations I left out. Below are some of my main principles when trying to decide optimally.

• Make sure you are asking the right question. This is the main premise of the blog; If you don't ask the right question, you are unlikely to get the right answer. In the gym example, I was choosing the best gym for me. The process would have been completely wrong if I was picking a place to work out with a friend or to make a recommendation to my parents.
• Figure out the range of possible outcomes. If all of the choices lead to the same outcome, why waste any time deciding between them? If the outcomes are on a wide spectrum from terrible to fantastic, it will be worthwhile to spend some time eliminating possibilities (or defining criteria for an acceptable choice. More on that later).
• Keep in mind what "approximately the best" means.  If you are making a decision with a lot of uncertainty, trying to find the absolute best choice is likely to be a waste of time since you don't know how the options truly compare.
• Target low-hanging fruit first. If you start with a set of possibilities, the order you eliminate options matters (at least when you are trying to decide optimally). In the gym example, we put off the time-consuming task of calling each place to find out if they had a pool until after we had made a short list of those within a two mile radius of us.
• Know when to stop. Once you have a set of options that are approximately the best, it is no longer worth it to spend a lot of time making your final selection. I will sometimes pick an arbitrary criteria to justify whichever choice I want to make at that point (they were the only gym with pretty paintings in the changing rooms).
• You don't have to consider every option. "Satisficing" means you choose the first option you come across that satisfies a set of requirements. This technique can be used at any point in the decision-making process. In the gym example, you might visit gyms that passed the distance and pool criteria, and pick the first one you liked. 

Those are the main tricks I use, whether I am deciding which type of lettuce to buy at the grocery store, or which graduate school to go to. The last tip I have is to try to develop a process you can be happy with ex-poste (after the fact). Occasionally I participate in economics experiments. While I might actually be somewhat risk averse, I usually choose to maximize my expected value since that is objectively the 'best' decision.

Post your tips in the comments!